1. Field of the Invention
The present invention relates to a method for performing a simulation of a semiconductor integrated circuit taking into consideration its manufacturing fluctuations.
2. Description of the Related Art
In the optimizing design or statistical analysis of a semiconductor integrated circuit, a massive amount of time is required for the computation of circuit characteristics for its analysis. For this reason, one of problems associated directly with improvement of the design quality and manufacturing yield is to minimize the computation time.
Conventional methods for performing a simulation of a semiconductor integrated circuit include a worst case simulation as a general method in which variation ranges are given to element parameters. In the worst case simulation, a vertex method or a moment method is often used. In the vertex method, the distributions of statistical parameters are all regarded as uniform distributions and one of vertexes in a parameter variation region is taken as a worst case. This worst case simulation method requires a less amount of computation but disadvantageously fails to take correlation between parameters into consideration, which leads to an overestimated or underestimated result. The moment method, on the other hand, can take the correlation between parameters into account but has a limitation that circuit characteristics must be ensured to be linear, for which reason this method requires great care when it is actually employed.
Meanwhile, in the case of this prior art such as disclosed in Japanese Patent Laid-Open Publication No. 348683/94, as shown in FIG. 1, items for consideration or examination such as amplification gain and harmonic distortion factors and parameters having variation ranges for common-emitter current transfer ratio hfe and semiconductor resistance of a transistor are input from an input device 304, and a probability interpolation model forming section 301 finds sampling data which provide the maximum approximation accuracy from the parameters having variation ranges, and forms an interpolation model based on the found data. Next, a statistical analysis section 302 determines a worst case based on the Monte-Carlo simulation with use of the interpolation model and the result is displayed by a result display section 303.
The aforementioned prior art can form an interpolation model with a less amount of computation by determining sampling data that provides a maximum approximation accuracy, with the result that analysis accuracy can be maintained with a smaller number of simulating operations. However, this method is disadvantageous in that the statistical analysis eventually uses Monte-Carlo simulation and thus requires a considerable number of simulating operations to secure a sufficiently improved approximation accuracy, though the method uses fewer computing operations than the general Monte-Carlo simulation.
For example, the number N of simulating operations required for an average error f obtained through the simulation to be within .+-.10% of population mean F, is about 100 when 3.sigma.=1 in an expression (1) which follows. ##EQU1## where, F denotes a population mean of characteristic (f), f is a mean of simulations, 3.sigma. is a parameter variation range, and N is a simulation frequency.
Since a semiconductor integrated circuit has manufacturing fluctuations, parameter variation ranges are given to elements on the semiconductor integrated circuit. The variation ranges include an absolute variation range defined by maximum and minimum element parameter variations and a relative variation range defined by aligned elements which are positioned adjacent to each other on the semiconductor integrated circuit and are regarded as aligned ones when they have the same structure and shape. In the relative variation range, a difference between the values of a parameter of the aligned elements is defined as its variation range, because the aligned elements are influenced by manufacturing fluctuations to the same extent and thus have nearly the same element parameter value. In general, the relative variation range is narrower than the absolute variation range.
The prior art has disadvantages in that computation to form the interpolation model is required in addition to the simulation. As a result, when the aforementioned relative variation range is taken into account, the computation to form the interpolation model disadvantageously becomes more difficult.